Cornyn, the chairman of the National Senatorial Campaign Committee (NRSC), said it'd be a poor sign for the GOP if a split field led to Democratic candidate Scott McAdams winning the state's Senate race.

"Frankly, that would be a disaster for us, if the Democrats won Alaska," Cornyn said during an appearance on MSNBC.

Polls show Murkowski and Miller locked in a virtual dead heat for the general election, as the NRSC goes on air in the state in support of Miller. The ad will cast Miller, the Tea Party-backed candidate, in a positive light while highlighting negative aspects of McAdams's record, Cornyn said.

Cornyn said he believed the new crop of Tea Party candidates, who beat many of the incumbents and highly recruited candidates sought by the NRSC in primary races, were an asset to the GOP in the closing days of the race.

The Texas Republican did continue to acknowledge, though, Republican Christine O'Donnell's difficulty in Delaware's Senate race, where she was unable to name a Democratic senator with whom she'd be able to work.

"It tells me that she's new to the kind of scrutiny that she's getting," Cornyn said.